Characterization of White Matter Degeneration in Elderly Subjects by Magnetic Resonance Diffusion and FLAIR Imaging Correlation

Relaxations Times

Let $T_1^{WM}$ and $T_2^{WM}$ be the longitudinal (T1) and transverse (T2) relaxation time of the normal WM, respectively, and $T_1^{\mathit{CSF}}$ and $T_2^{\mathit{CSF}}$ be the T1 and T2 for CSF accordingly. Under the condition of fast water exchange, the effective relaxation times of the mixed WML signal can be estimated (Kamman et al., 1988) as $1/T_1^{\mathit{WML}}=(1-f)/T_1^{WM}+f/T_1^{\mathit{CSF}}$ and $1/T_2^{\mathit{WML}}=(1-f)/T_2^{WM}+f/T_2^{\mathit{CSF}}$, where the coefficient f = [0,1] is the partial volume fraction of the CSF pool, representing the severity of WML degeneration on the continuum from normal WM (f=0) to pure CSF (f =1).

Fig. 1(a) shows the simulated T1 and T2 curves with respect to the WML severity f using experimental tissue relaxation parameters of normal WM and CSF at 4T (Rooney et al., 2007). In Fig. 1(b) the joint relaxation times (T1, T2) are illustrated to better capture the change of T2, which is generally much smaller than T1 in magnitude. A slightly curved (T1, T2) trajectory represents discordance of T1 and T2 prolongations in the lesion progression, i.e. the increasing partial volume fraction of free water pool.

FLAIR Measurements

The signal intensity of white matter lesions (WML) in a T2-weighted fluid-attenuated inversion recovery (FLAIR) experiment can be expressed (Rydberg et al., 1995) by

where TI, TR and TE are the parameters of inversion time, repetition time and echo time used in the FLAIR experiment, respectively. The parameter ρ_1H represents the effective WML proton density, which is used to correct the signal intensity as a function of the volume fraction, f such that ${\rho }_{1\mathbf{H}}=(1-f)·{\rho }_{1\mathbf{H}}^{WM}+f·{\rho }_{1\mathbf{H}}^{\mathit{CSF}}$, where ${\rho }_{1\mathbf{H}}^{WM}$ and ${\rho }_{1\mathbf{H}}^{\mathit{CSF}}$ are the proton densities in WM and CSF water pools, respectively.

In Fig. 2(a), the surface of FLAIR signal intensities are plotted as a function of T1 and T2, defined in the rectangular area spanned by diagonal vertexes ( $T_1^{WM},T_2^{WM}$) and ( $T_1^{\mathit{CSF}},T_2^{\mathit{CSF}}$). The surface-embed curve connecting the WM and CSF vertexes is determined by the (T1, T2) trajectory of WM degeneration shown in Fig. 1(b). The estimated FLAIR intensities of the WML with respect to the lesion severity (as represented by the free water-pool volume fraction f) are plotted in Fig. 2(b). A non-monotonic FLAIR intensity curve is plotted against the WML severity, where the effects of changing proton densities in WML are corrected by considering the proton density differences in WM and CSF pools. Maximum FLAIR intensity is reached when f is approximately equal to 0.7 for the given experimental imaging parameters described in Methods. Imaging noise, if considered, is added onto M_FLAIR regardless of the lesion severities.

DTI Measurements

Let D^WM and D^CSF be the diffusion tensors of the normal WM and pure CSF compartment, respectively, in the static dual water pool model for WML. Under the fast-exchange condition again, the overall effective diffusion-weighted signal of the WML in a diffusion-weighted spin-echo experiment can be estimated (Hsu and Mori, 1995; Alexander, 2000) as

in which V is the vector of diffusion gradient of a b value, and the reference signal of WML is given by $S_0^{\mathit{WML}}=(1-f)·S_0^{WM}+f·S_0^{\mathit{CSF}}$. Thus, a set of diffusion-weighted signals $S_i^{\mathit{WML}}$, (i = 1, 2, … n), (n>=6) can be obtained based on a set of non-coplanar vectors V_i, (i = 1, 2, … n), and the corresponding diffusion tensor and indices can then be estimated (Le Bihan et al., 2001). Imaging noise, if considered, is added onto S^WML and $S_0^{\mathit{WML}}$ independently.

For both noise free and noisy conditions, Fig. 3 shows the curves of fractional anisotropy (FA) and mean diffusivity (MD) indices (Le Bihan et al., 2001) of the effective WML diffusion tensor as the function of the lesion severity as represented by the free water-pool volume fraction f when using realistic diffusion imaging parameters as described in Methods. In the noise-free condition (Fig. 3a and b), monotonic changes of FA and MD are observed with respect to increasing WML severity, and FA curves show an insensitivity to the b value. In the condition with simulated additive noises (Fig. 3c and d), stronger fluctuations appear in FA curves and higher WML severities.

DTI-FLAIR Correlations

Assume that the variability of DTI and FLAIR signals of WML is caused by the lesion severity and additive random noise, thus the correlations between DTI and FLAIR measurements would vary at different lesion severities due to the mismatched patterns of the two modalities. As illustrated in Fig. 4, a total of 20 independent trials are repeated to obtain the mean value and standard deviation of the DTI-FLAIR correlation in 10 successive severity intervals of f = [0 0.1], [0.1, 0.2], … [0.9, 1.0]. The noise levels of DTI and FLAIR signals are specified according to our experimental data, namely a signal-to-noise ratio (SNR) of 60:1 and 80:1 for the FLAIR and DTI reference images (b=0), respectively. Other simulation parameters (e.g. b value, encoding directions, relaxation times, etc.) are also set as the same as the in vivo experiments (see Methods).

As shown in Fig. 4 the correlation between FLAIR and DTI measures disappear for lesions as the lesion severity reaches 0.7, i.e. the water pool in WML is 70% free, and 30% bound water. For MD, an inverse correlation emerges as WML severity further increases. In contrast, the correlation between FA and FLAIR remains small as WML severity increases continues to grow because noise dominates FA more than FLAIR, especially for higher WML severities (See Fig. 3). The higher vulnerability of FA to image noises than MD (Papadakis et al., 2000) is also indicated by the larger error bars for the FA-FLAIR correlation coefficients in Fig. 4.

Image Acquisition

Thirty-three cognitively normal elder volunteers (Female=19), with mean age of 71±10 years and mean Mini Mental State Examination (MMSE) (Folstein et al., 1975) scores of 27.6±3.3 recieved MRI scans at 4 Tesla (Siemens). The MRI scanner was equipped with a birdcage transmit and an 8-channel receiver coil in a single housing. DTI, FLAIR, and T1-weighted imaging (MPRAGE) data were acquired in a single session on each subject. EPI-based DTI data were acquired using parallel imaging (GRAPPA) (Griswold et al., 2002) with two fold acceleration. Other parameters were: TR/TE = 6s/77ms, matrix size = 128×128×40 yielding 2×2×3 mm nominal resolution, and 6 diffusion encoding directions with b=800 s/mm². DTI acquisitions were repeated 4 times to boost the signal to noise ratio (SNR). The FLAIR parameters were: TR/TI/TE = 5s/1.9s/355ms, echoes=209 per segmented k-space sampling, flip angle =180 degrees, and matrix size=256×192×60 yielding 1.1×1.1×2 mm spatial resolution. T1-weighted anatomical images were also acquired for image normalization as described below. Experiments were performed according to the guidelines of institutional research board (IRB) of University of California San Francisco, and Veterans Affair Medical Center of San Francisco. Normal cognitive functioning of subjects was assessed by a short battery of neuropsychological tests: MMSE, California Verbal Learning Test (short form), Rey–Osterrieth complex figure, Verbal Fluency, Wechsler Adult Intelligence Score (digit symbol, digit span), as described in recent publication of our lab (Mueller et al., 2008). Subjects, who received − 1.5 standardized score or less in more than two of these tests, were excluded from the study.

DTI Processing

After eddy current correction (Bodammer et al., 2004), the diffusion tensor and the spatially invariant summary measures fractional anisotropy (FA) and mean diffusivity (MD) were calculated offline for each voxel with the FMRIB Software Library (FSL) (www.fmrib.ox.ac.uk/fsl/). DTI processing tools for tract-based spatial statistics (TBSS) (Smith et al., 2006) were used for the spatial normalization procedure of the DTI data in following steps: (i) A representative subject (female, 70 yrs) was selected as the co-registration “target” to which the 3D FA maps of all subjects were aligned by the nonlinear registration procedure in TBSS; (ii) The aligned FA maps were interpolated to 1×1×1 mm resolution, and spatially normalized by the same nonlinear coregistration program with respect to a T1-weighted template in Talairach space (Chau and McIntosh, 2005); and (iii) For each subject, the MD map was spatially normalized to the Talairach space by the same transformation pipeline as that was estimated in the FA map normalization in Steps (i) and (ii). In order to retain a full voxelwise mapping for WM, no WM skeletonlization procedure was applied in this study.

FLAIR Processing

The effects of B1-field inhomogeneities on the FLAIR intensities were adjusted using a non-parametric high order co-occurrences technique (Hadjidemetriou et al., 2007). WML regions with abnormal hyperintensity (defined as 25% higher than the average intensity of surrounding WM tissue in FLAIR) were extracted from the intensity corrected FLAIR images using the graph cuts algorithm (Boykov et al., 2001). The FLAIR and T1 weighted MPRAGE images of each subject were first registered to each other using a rigid transformation, and then spatially normalized to a T1 template as used in DTI using a fluid-based nonlinear registration technique (Christensen et al., 1997). Spatial normalized WML maps were obtained by following the T1 image transformation pipeline as described in (Joshi et al., 2003). Both WML intensity (i.e. the FLAIR hyperintensity compared with normal WM) and total WML volume (i.e. the number of voxels of extracted WML regions) were interchangeably used as measure of WML severity.

Due to the susceptibility-induced geometrical distortions in EPI-based DTI images, as well as the lack of WM tract contrast in the T1 images, misalignments between DTI and FLAIR images may remain (empirically less than 4 mm). To improve alignment, we manually adjusted the T1 template for FLAIR registrations using affine adjustments (< 1%), which generally reduced discrepancy to < 2 mm, as assessed by the discrepancy between mean FA map and the T1-template in major WM regions like corpus callosum (See Fig. 5 and results for justification).

Correlation Analysis

For spatially normalized images, the DTI-FLAIR correlation analysis was performed across subjects in two ways: (1) Total WML volume (measured in the segmented WML map in the normalized space) was correlated to the FA or MD value at each image voxel for all subjects; and (2) WML intensity (measured in the segmented WML map) was correlated to the FA or MD value at each voxel for all subjects. The Pearson product moment correlation (Neter et al., 1990) was used to test for significant associations between FLAIR and DTI. Before the correlation coefficient was estimated, age and gender were used as independent variables in a multivariate linear regression program (Kamman et al., 1988) to adjust for their effects to the DTI data on a voxelwise basis. The correlation clusters were picked up at p<0.001 for all normalized DTI image voxels at 1 mm³ resolution.

Computer Simulations

The dual water pool model described in the Theory section was used to simulate the progression of WM degeneration by increasing the volume fraction of unbound water, as is found in CSF. Relaxation times at 4T of normal WM (T1/T2=1043/65ms) and pure CSF (T1/T2=4500/120ms) were assumed for the 2 water pools (Kamman et al., 1988; Rooney et al., 2007). The proton density differences between the dual water pools were assumed to be governed by the mass fractions of water content of 71% and 100%, for normal WM and pure CSF, respectively (Curry et al, 1990). For DTI, axially symmetrical diffusion tensors in each compartment were assumed having eigenvalues (0.95, 0.35, 0.35)×10⁻³ and (2.3, 2.3, 2.3)×10⁻³ mm²/s, respectively (Le Bihan et al., 2001). A fast water exchange was assumed in signal estimation for both FLAIR and DTI based on the in vivo imaging parameters listed above. Gaussian distributed noise was added to simulate an SNR of 60:1 for FLAIR and an SNR of 80:1 for DTI reference images (corrected after repetitions). These SNR values were based on experimental in vivo raw data. The b value of 1000 s/mm² was used to calculate the FA and MD measurements. Ten successive WML severity intervals of f = [0, 0.1], [0.1, 0.2], … [0.9, 1.0] were used to estimate the DTI-FLAIR correlations for different severities. A total of 20 independent trials were repeated to obtain the mean and standard deviation of the correlation coefficients between the two modalities in each severity interval.

Experimental Mean FA and mean WML maps

In Fig. 5(a) and (b), the mean FA map of all subjects at threshold of FA>0.35 for major WM tracts is superimposed in color on the grayscale T1 templates to demonstrate the cross-modality coregistration quality. In column (a), the background T1 template used for the DTI spatial normalization shows a moderate misregistration to the mean FA map, especially near the corpus callosum. In column (b), the manually aligned T1 template demonstrates reduced misregistration to the same mean FA map. In column (c), the mean WML intensity map of all subjects is superimposed in color on the aligned T1 template, onto which all FLAIR images and WML maps have been registered. Because of the MRI similarities between FLAIR and T1, the registration between the two is generally much better than between DTI and T1. Therefore, the insufficient coregistration between DTI and FLAIR can be primarily attributed to the DTI-to-T1 template misalignments.

Correlations between DTI and WML Volume

Fig. 6 shows the profile of voxelwise correlations between the DTI index (FA or MD) and the total WML volume, overlaid on either mean FA or mean WML intensity maps. The correlation clusters are selected at threshold p<0.001 using blue and red to represent negative and positive correlations, respectively. This shows that significant correlations between DTI and WML volumes primarily appear on or adjacent to the WM regions where the mean WML intensities are moderately high, and that no significant correlation clusters are detected in the regions where the mean WML intensities are the highest, as demonstrated in periventricular regions. Compared to the correlations between FA and WML volume, which are dominantly negative, the correlations between MD and WML volume are generally positive and occur on similar and slightly wider areas, indicating a stronger MD-WML correlation. In Fig. 6(b) and (d), the same correlation clusters as shown in (a) and (c) are imposed on the mean WML map to visually enhance the spatial correspondence with respect to the corresponding WML intensities. In general, FA and MD exhibit consistent correlations with the total WML volume with opposite signs, partially overlapping the WML regions. It is interesting to observe that these clusters distribute on “boundary” WML areas, rather than concentrate on the most intense WML regions.

Correlations between DTI and WML intensity

Using a similar display, the voxelwise correlations between the DTI index (FA or MD) and the WML intensity are illustrated in Fig. 7. The axial slice used in the lower row is identical to the axial slice in Fig. 6. The blue clusters in columns (a) and (b) are negative FA-WML intensity correlations selected at p<0.001, overlaid on the mean FA and mean WML intensity maps, respectively. The red clusters in columns (b) and (c) represent the positive correlations between MD and WML intensity, displayed on the background of mean FA and mean WML intensity maps. The similarity of cluster distributions in Fig. 6 and Fig. 7 suggest that the WML intensity and the total WML volume are associated in their correlations with the DTI measurements. Comparatively, DTI to WML intensity correlations are more significant and distributed slightly closer to the major WM tracts than the DTI to WML volume correlations. Consistent to the results shown in Fig. 6, the DTI-WML intensity correlation clusters in Fig. 7 exhibit a pattern of partial overlapping over the mean WML map. Again, these clusters appear only on the regions where the WML intensities are moderate rather than the areas where the WML intensities are particularly high.